The former NAB private banker, Deutsche Bank vice-president and Rothschild Australia senior manager was elected in 2016 and lives in Malvern, in the heart of the electorate.
Liberal sources said on Sunday that defeated state MP John Pesutto wanted to run in the seat but felt he couldn’t put himself forward because of the push for greater female representation in the party’s federal ranks.
The former shadow attorney-general was a shock loss in November’s state poll.
Jess Wilson, a Business Council of Australia director and former adviser to Treasurer Josh Frydenberg, is considering entering the race, a possible frontrunner if Senator Hume decides to stay in the upper house.
Trade expert and former ministerial adviser Zoe McKenzie; paediatrician and defeated state candidate Katie Allen; and former Victorian upper house MP Margaret Fitzherbert are also being discussed.
Other names being floated included Stonnington councillor Marcia Griffin, businesswoman Caroline Elliott and former Coalition staffer Holly Byrne.
The seat has long been considered safe for the Liberal Party but could be at risk this year.
Polling in December showed Labor leading in Higgins on a two-party-preferred basis by 52.2 per cent to 47.8 per cent.
Ms O’Dwyer replaced her former boss Peter Costello in Higgins in a byelection in 2009.
The 41-year-old said she was quitting to be closer to her young family and her desire to have a third child, later confirming she had dealt with a miscarriage while in Canberra.
A leading moderate and one of the most senior Liberal women, Ms O’Dwyer’s move to quit risks leaving the Coalition without any female MPs from Victoria and boosted Labor’s criticism of the Coalition’s male-dominated ranks.
“She’s made her choice and I was pleased to be standing with her in that choice,” he said on Sunday.
Some Liberals say a move by Senator Hume could pave the way for Tony Abbott’s former chief-of-staff Peta Credlin to enter the Senate.